What question did this study set out to answer?

This research aims to generalize representations of pleated surfaces using Borel Anosov representations.

July 3, 2026Proceedings of the London Mathematical Society1 citationsOpen Access

d‐Pleated surfaces and their shear‐bend coordinates

SMSara MaloniUniversity of Virginia GMGiuseppe MartoneSam Houston State University FMFilippo MazzoliUniversity of California, Riverside

Key Points

This research aims to generalize representations of pleated surfaces using Borel Anosov representations.
Developed representations that connect surface groups to pleated surfaces.
Provided a holomorphic parameterization of the space of pleated surfaces with a pleating locus.
Extended existing frameworks from Bonahon and Dreyer for further representations.
Established a new class of representations that are Borel Anosov with respect to a maximal geodesic lamination.
Identified conditions under which these representations can be holomorphically parameterized.

Abstract

Abstract In this article, we single out representations of surface groups into that generalize the well‐studied family of pleated surfaces into . Our representations arise as sufficiently generic ‐Borel Anosov representations, which are representations that are Borel Anosov with respect to a maximal geodesic lamination . For fixed and , we provide a holomorphic parameterization of the space of ‐pleated surfaces with pleating locus that extends both work of Bonahon for pleated surfaces and Bonahon and Dreyer for Hitchin representations.

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